Modeling Solute Transport and Urine Concentrating Mechanism in the Rat Kidney The goal of this proposal is to use mathematical modeling to investigate aspects of the renal trans- port and dynamics, with an ultimate goal of gaining a better understanding of the mammalian urine concentrating mechanism and solute cycling. Mathematical models of renal tubules and microvessels, coupled with explicit analysis and numerical methods for solving dierential equations, will be used in the following studies: (I) A model of the urine concentrating mechanism of the renal medulla in the rat kidney that represents the relative positions of the tubules and vessels will be developed and used to test the hypothesis: the urine concentrating mechanism of the renal inner medulla of the rat kidney arises from solute mixing in the interstitium, and that mechanism may be comprised of four countercurrent systems, based on the specic 3-dimensional relationships among tubules and vessels. (II) A specic aspect of the 3-dimensional organization in the inner medulla will be considered: interstitial nodal spaces that are bordered by collecting ducts, ascending vasa recta, and ascending thin limbs. A compartment model will be used to test the hypothesis that these microdomains may be essential mixing nodes for targeted delivery and interaction of specic solutes. (III) A dynamic model of the urine concentrating mechanism will be developed and used to track solute (urea, in particular) cycling, to study residence times of solutes, and to study the transient eects of urea loads. The ultimate goal is to gain a better understanding of urea recycling in the renal medulla, and the role of medullary 3-dimensional structure and countercurrent tubular conguration in urea management under physiologic and pathophysiologic conditions. (IV) A slice model of the inner stripe of the rat outer medulla, together with a detailed representation of the epithelial transport processes of the thick ascending limb cell, will be used to study the energy eciency and sodium transport of the thick ascending limbs.